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2 years ago

10

Determine if the function is continuous to its domain

1 answer:

Maurinko [17]2 years ago

6 0

Yes, it is continuous to its domain

<h2>Explanation:</h2><h2></h2>

In order to find the domain of the function we need to get the restrictions:

1. From natural log:

$x>0$

2. From quotient:

$x\neq 0$

Matching these two restrictions the domain is:

$x\in (0,\infty)$

So the function is continuous to its domain because is defined for every x-value in the interval $(0, \infty)$ )

<h2>Learn more:</h2>

Functions: brainly.com/question/12891789

#LearnWithBrainly

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A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean isx⎯ ⎯ x¯ = 840 and

gayaneshka [121]

Answer:

$(832.156, \ 847.844)$

Step-by-step explanation:

Given data :

Sample standard deviation, s = 15

Sample mean, $\overline x = 840$

n = 23

a). 98% confidence interval

$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$

$$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}$

$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$

$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$

∴ $E = 2.508 \times \frac{15}{\sqrt{23}}$

$E = 7.844$

So, 98% CI is

$(\overline x - E, \overline x + E)$

$(840-7.844 , \ 840+7.844)$

$(832.156, \ 847.844)$

4 0

2 years ago

What is the inverse of the function f(x) = 2x – 10?

noname [10]

Answer:

The inverse f-1(x) = ( x + 10)/2.

Step-by-step explanation:

f(x) = 2x - 10

Find x in terms of f(x):

2x = f(x) + 10

x = (f(x) + 10))/ 2

Replace x by the inverse f-1(x) and f(x) by x:

f-1(x) = (x + 10)/2.

7 0

3 years ago

LMN is a right-angle triangle. Angle NLM=90. PQ is parallel to LM. The area of triangle PNQ is 8cm^2. The area of triangle LPQ i

likoan [24]

Answer:

The area of LQM is $48cm^2$

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

$Area = \frac{1}{2} * PQ * PN$

Substitute 8 for Area

$8 = \frac{1}{2} * PQ * PN$

$PQ * PN = 16$

The area of LPQ is calculated as:

$Area = \frac{1}{2} * PQ * LP$

Substitute 16 for Area

$16= \frac{1}{2} * PQ * LP$

From the attachment:

$PN + LP =LN$

Make LP the subject

$LP = LN -PN$

So:

$16= \frac{1}{2} * PQ * (LN -PN)$

We have:

$16= \frac{1}{2} * PQ * (LN -PN)$ and $PQ * PN = 16$

Equate both expressions:

$\frac{1}{2} * PQ *(LN - PN) = PQ * PN$

Divide both sides by PQ

$\frac{1}{2} (LN - PN) = PN$

Multiply both sides by 2

$LN - PN = 2PN$

$LN= 3PN$

Since PNQ is similar to LNM, the following equivalent ratios exist:

$\frac{LM}{PQ} = \frac{LN}{PN}$

Substitute $LN= 3PN$

$\frac{LM}{PQ} = \frac{3PN}{PN}$

$\frac{LM}{PQ} = 3$

$LM = 3PQ$

Area of LQM is:

$Area = \frac{1}{2} * LM * LP$

This gives:

$Area = \frac{1}{2} * 3PQ * LP$

$Area = 3 *\frac{1}{2} *PQ * LP$

Recall that:

$16= \frac{1}{2} * PQ * LP$

So:

$Area = 3 *16$

$Area = 48cm^2$

5 0

2 years ago

Round 111.11111 to the nearest ten thousandth.

marishachu [46]

One tenth is 0.1. One hundredth is 0.01. Therefore, one ten thousandth is 0.00001. The answer is 111.11111.

5 0

2 years ago

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2 x [(29-6)-[(6+5)]<br> please show work!

Anika [276]

Answer:

Not sure, read steps.

Step-by-step explanation:

First do the ()

29 - 6 = 23

6 + 5 = 11

SUBTRACT THE INTEGERS:

23 - 11 = 12

So, 2 x 12 = 24.

4 0

2 years ago

Read 2 more answers